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This document discusses key concepts related to similar polygons including: - Polygons are similar if corresponding angles are congruent and corresponding sides are proportional. - The scale factor is the ratio of corresponding sides in similar figures. - Scale drawings use proportions to relate lengths in a drawing to actual lengths, and are used in applications like poster design.

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6 1 coordinate proofs

Analytic geometry uses algebraic methods to study and prove geometric problems using coordinates. This chapter discusses using coordinate proofs to prove theorems from geometry. It provides instructions on how to construct a coordinate proof by drawing and labeling a diagram, listing given information, stating what will be proved, using algebra to add to the diagram and prove the statement, and writing a conclusion. Common algebraic methods used in proofs include the distance formula, identifying parallel and perpendicular lines, and finding midpoints. Examples provided are proving properties of right triangles, trapezoids, and triangles.

Coordinate proofs

This document discusses using coordinate geometry to prove theorems about shapes in geometry. It states that it is easiest to work with shapes that are aligned with the x- and y-axes, like right triangles oriented with legs parallel to the axes or trapezoids and parallelograms aligned with the axes. It provides examples of using coordinates to prove properties about the midpoint of a hypotenuse, the median of a trapezoid, and the altitudes of a triangle. Finally, it lists five methods used in coordinate proofs, such as using the distance formula to prove line segments are equal in length.

Plane Geometry

This document provides an overview of key concepts in plane geometry covered in Chapter 5, including points, lines, planes, angles, parallel and perpendicular lines, triangles, polygons, coordinate geometry, congruence, transformations, and tessellations. Specific topics discussed include classifying angles, properties of parallel lines cut by a transversal, the triangle sum theorem, types of triangles and polygons, finding total angle measures of polygons, and using coordinate geometry. Homework problems are provided at the end of sections for additional practice.

Assignmnt 1 fdp

This document provides an introduction and overview of graph theory. It defines some basic concepts such as vertices, edges, degrees of vertices, paths, walks, trees, and connectedness. It also introduces more advanced topics like isomorphic graphs, subgraphs, complements of graphs, bipartite graphs, and diameters of graphs. Finally, it discusses some applications of graph theory in fields like chemistry, physics, biology, computer science, operations research, maps, and the internet.

Quadrilaterals - Evaluation

This document provides an evaluation for Ms. Reybeth D. Racelis and includes drills to identify the best word to describe various geometric terms. Fifteen terms related to lines, angles, polygons and quadrilaterals are listed, and students are directed to write the best describing word for each on their answer sheet. The evaluation and drills are intended to assess the student's readiness and knowledge of basic geometry concepts.

Similar Triangles

The document discusses similar triangles and how to determine if two triangles are similar. It explains that two triangles are similar if corresponding angles are congruent. It provides examples of using the Angle-Angle similarity criterion to show triangles are similar and using ratios to find a missing side of a similar triangle. The lesson covered properties of congruent and similar triangles, various similarity criteria like AA and SAS, and how to prove triangles are similar.

joshua benny hinn ppt 1 triangles for class x

This document defines and describes different types of triangles. It discusses the key properties of triangles including that the sum of the interior angles is always 180 degrees. It also defines the six main types of triangles: equilateral, isosceles, right, scalene, acute, and obtuse. Additionally, it presents the basic proportionality theorem and its converse, which relate parallel lines drawn to the sides of a triangle.

Geometry in the Real World Project

The document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, cylinders, spheres, cubes, pyramids and cones. It provides the formal definitions for these terms and shapes as undefined or basic terms in geometry without thickness or size limitations that extend indefinitely in some cases. The project involves taking photos of these shapes in the real world during a family trip to Austria.

6 1 coordinate proofs

Analytic geometry uses algebraic methods to study and prove geometric problems using coordinates. This chapter discusses using coordinate proofs to prove theorems from geometry. It provides instructions on how to construct a coordinate proof by drawing and labeling a diagram, listing given information, stating what will be proved, using algebra to add to the diagram and prove the statement, and writing a conclusion. Common algebraic methods used in proofs include the distance formula, identifying parallel and perpendicular lines, and finding midpoints. Examples provided are proving properties of right triangles, trapezoids, and triangles.

Coordinate proofs

This document discusses using coordinate geometry to prove theorems about shapes in geometry. It states that it is easiest to work with shapes that are aligned with the x- and y-axes, like right triangles oriented with legs parallel to the axes or trapezoids and parallelograms aligned with the axes. It provides examples of using coordinates to prove properties about the midpoint of a hypotenuse, the median of a trapezoid, and the altitudes of a triangle. Finally, it lists five methods used in coordinate proofs, such as using the distance formula to prove line segments are equal in length.

Plane Geometry

This document provides an overview of key concepts in plane geometry covered in Chapter 5, including points, lines, planes, angles, parallel and perpendicular lines, triangles, polygons, coordinate geometry, congruence, transformations, and tessellations. Specific topics discussed include classifying angles, properties of parallel lines cut by a transversal, the triangle sum theorem, types of triangles and polygons, finding total angle measures of polygons, and using coordinate geometry. Homework problems are provided at the end of sections for additional practice.

Assignmnt 1 fdp

This document provides an introduction and overview of graph theory. It defines some basic concepts such as vertices, edges, degrees of vertices, paths, walks, trees, and connectedness. It also introduces more advanced topics like isomorphic graphs, subgraphs, complements of graphs, bipartite graphs, and diameters of graphs. Finally, it discusses some applications of graph theory in fields like chemistry, physics, biology, computer science, operations research, maps, and the internet.

Quadrilaterals - Evaluation

This document provides an evaluation for Ms. Reybeth D. Racelis and includes drills to identify the best word to describe various geometric terms. Fifteen terms related to lines, angles, polygons and quadrilaterals are listed, and students are directed to write the best describing word for each on their answer sheet. The evaluation and drills are intended to assess the student's readiness and knowledge of basic geometry concepts.

Similar Triangles

The document discusses similar triangles and how to determine if two triangles are similar. It explains that two triangles are similar if corresponding angles are congruent. It provides examples of using the Angle-Angle similarity criterion to show triangles are similar and using ratios to find a missing side of a similar triangle. The lesson covered properties of congruent and similar triangles, various similarity criteria like AA and SAS, and how to prove triangles are similar.

joshua benny hinn ppt 1 triangles for class x

This document defines and describes different types of triangles. It discusses the key properties of triangles including that the sum of the interior angles is always 180 degrees. It also defines the six main types of triangles: equilateral, isosceles, right, scalene, acute, and obtuse. Additionally, it presents the basic proportionality theorem and its converse, which relate parallel lines drawn to the sides of a triangle.

Geometry in the Real World Project

The document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, cylinders, spheres, cubes, pyramids and cones. It provides the formal definitions for these terms and shapes as undefined or basic terms in geometry without thickness or size limitations that extend indefinitely in some cases. The project involves taking photos of these shapes in the real world during a family trip to Austria.

Similarities and congruences

This document discusses similarity and congruence of plane figures. It defines similar figures as those where corresponding angles are equal and corresponding side ratios are equal. Examples of similar figures include rectangles where the ratio of length to width is equal. The document provides examples of similar and congruent triangles and quadrilaterals. It also lists key terms and learning objectives related to identifying similar and congruent plane figures based on corresponding side lengths and angles.

7 4 Similar Triangles and t-5

This document discusses three rules for determining if triangles are similar: the AA Similarity Postulate, SAS Similarity Theorem, and SSS Similarity Theorem. It provides examples of applying each rule to determine if triangles are similar, and if so, writing the similarity statement and ratio.

Congruent and similar triangle by ritik

This document discusses congruent and similar triangles. It begins by introducing the concepts and explaining how recognizing similar shapes can simplify design work. It then defines congruent triangles as having equal sides and angles, while similar triangles have the same shape but not necessarily the same size. The document notes that two figures can be similar but not congruent, but not vice versa. It provides examples of similar and congruent figures. It further explains that similar triangles have corresponding sides and angles in the same locations that are in the same ratio. It demonstrates using ratios and proportions to determine unknown side lengths in similar figures. Finally, it discusses ways to prove triangles are similar, including having congruent corresponding angles (AA similarity) or proportional corresponding sides (SS

Polygons b.ing math. citra

This document discusses polygons and tessellations. It defines polygons, their properties including interior angles and the relationship between number of sides and total interior angle measures. Regular polygons are introduced as those with all congruent sides and interior angles. Methods for drawing regular polygons using angles and a circumscribed circle are provided. Tessellations are defined as arrangements that cover a region without gaps or overlaps. Regular hexagons, squares, and equilateral triangles can tessellate on their own. Problem solving involves calculating the measure of each interior angle of a regular hexagon.

Math chart model lesson

This powerpoint is a good tool to use to reintroduce students to the parts of the reference chart, so that they can effectively use it.

Project report on maths

This document defines and explains properties of various quadrilaterals and triangles. It defines parallelograms, rectangles, rhombi, and trapezoids, listing their key properties such as opposite sides being parallel and congruent, opposite angles being congruent, diagonals bisecting each other, etc. It also defines scalene, isosceles, equilateral, acute, obtuse, and congruent triangles. Area formulas are provided for various shapes using base and height.

Obj. 17 Congruent Triangles

Identify congruent parts based on a congruence relationship statement
Identify and prove congruent triangles given
Three pairs of congruent sides (Side-Side-Side)
Two pairs of congruent sides and a pair of congruent included angles (Side-Angle-Side)

Triangles

1) The document discusses properties and theorems related to triangles, including similarity, congruence, medians, altitudes, angle bisectors, and the Pythagorean theorem.
2) It provides criteria for establishing similarity between triangles, including having equal corresponding angles or proportional corresponding sides.
3) Theorems are presented on parallel lines cutting across two sides of a triangle in the same ratio, and on perpendiculars drawn from right triangle vertices cutting the hypotenuse.

02 geometry

This document provides definitions and formulas for calculating geometric properties of basic two-dimensional shapes such as triangles, rectangles, circles, trapezoids, and parallelograms. It also includes formulas for calculating volumes and surface areas of three-dimensional objects like cubes, spheres, cylinders, cones, and pyramids. Additionally, it discusses properties related to angles of intersection for lines and parallel lines, angle relationships in triangles, similarity of triangles, and the Pythagorean theorem.

Modern Geometry Topics

This powerpoint includes:
Triangles and Quadrangles
Definition, Types, Properties, Secondary part, Congruency and Area
Definitions of Triangles and Quadrangles
Desarguesian Plane
Mathematician Desargues and His Background
Harmonic Sequence of Points/Lines
Illustrations and Animated Lines.

Similar Triangles Notes

1) Congruent and similar triangles can be used to simplify design and calculations. Congruent triangles have equal sides and angles, while similar triangles have the same shape but not necessarily the same size.
2) Corresponding sides and angles of similar triangles have the same ratios. Ratios can be used to determine unknown side lengths.
3) Triangles are similar if two angles are congruent (AA similarity) or if all three sides are proportional (SSS similarity).

Geometry In The Real World

This document defines common geometric terms including point, line, plane, angle, perpendicular lines, parallel lines, triangles, right triangles, pentagons, hexagons, squares, rectangles, trapezoids, parallelograms, circles, cylinders, spheres, pyramids, cubes, and cones. It provides the basic definitions for these terms, stating that points have no size, lines have no thickness, planes extend forever, and polygons have a certain number of sides.

Triangles X CLASS CBSE NCERT

This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of similar triangles, including the AAA, SSS, SAS, and AA similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles discussed include scalene, isosceles, equilateral, acute, obtuse, and right triangles.

Triangle ppt

This document provides an overview of triangles, including definitions, types, properties, secondary parts, congruency, and area calculations. It defines a triangle as a 3-sided polygon with three angles and vertices. Triangles are classified by side lengths as equilateral, isosceles, or scalene, and by angle measures as acute, obtuse, or right. Key properties discussed include the angle sum theorem, exterior angle theorem, and Pythagorean theorem. Secondary parts like medians, altitudes, perpendicular bisectors, and angle bisectors are also defined. Tests for triangle congruency such as SSS, SAS, ASA, and RHS are outlined. Formulas are provided for calculating the areas of

Triangles introduction class 5

This document discusses triangles and their properties. It defines a triangle as a shape with three connected line segments and three vertices. The key properties discussed are:
1) The sum of the three interior angles of any triangle is always 180 degrees.
2) For a shape to be a triangle, the length of any one side must be less than the sum of the other two sides.
3) Triangles can be categorized based on the lengths of their sides (scalene, isosceles, equilateral) or degrees of their angles (acute, right, obtuse).

Geometry In The Real World Project

The document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, spheres, cylinders, cones, prisms and more. It provides the key properties of each shape such as the number of sides, angles, parallel or perpendicular lines, and other distinguishing characteristics.

Lecture 4.4

This document discusses two postulates for proving triangles congruent: the Side-Side-Side (SSS) postulate and the Side-Angle-Side (SAS) postulate. It provides examples of proofs using each postulate, demonstrating how to prove triangles congruent by showing that three sides or two sides and the included angle are congruent between the two triangles. The document includes practice problems applying these postulate proofs.

Surface area of prisms and cylinders

This amazing power point will show you everything that you need to know about finding the surface area of prisms and cylinders. 7TH GRADE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

CLASS X MATHS

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in the same ratio. Similar triangles have the same shape but not necessarily the same size. The document provides examples of determining if triangles are similar by checking if their corresponding angles are equal. It also shows using scale factors to calculate missing side lengths in similar triangles using the Basic Proportionality Theorem.

5.1 Congruent Polygons

Two polygons are congruent if they have the same shape and size, with corresponding angles and sides in the same position. Congruent polygons have corresponding angles that are equal and corresponding sides that are equal. The student learns to write and interpret congruence statements between triangles using equal corresponding angles and sides, and to prove polygons are congruent using the definition of congruence.

J9 b06dbd

This document provides information about similar and congruent figures in geometry. It defines similar figures as those that have the same shape but not necessarily the same size, while congruent figures have both the same shape and the same size. Corresponding parts of similar figures, such as corresponding angles and sides, are identified and their properties are described. Examples are provided to demonstrate how to determine if figures are similar based on ratios of corresponding side lengths. Congruent figures are also discussed, noting that corresponding angles and sides of congruent figures are congruent. The document concludes with practice problems applying the concepts of similar and congruent figures.

440 Chapter 7 SimilaritySimilar Polygons7-2Objective.docx

440 Chapter 7 Similarity
Similar Polygons7-2
Objective To identify and apply similar polygons
A movie theater screen is in the shape of
a rectangle 45 ft wide by 25 ft high.
Which of the TV screen formats at the
right do you think would show the most
complete scene from a movie shown on the
theater screen? Explain.
Similar fi gures have the same shape but not necessarily the same size. You can
abbreviate is similar to with the symbol ,.
Essential Understanding You can use ratios and proportions to decide whether
two polygons are similar and to fi nd unknown side lengths of similar fi gures.
You write a similarity statement with corresponding vertices in order, just as you write
a congruence statement. When three or more ratios are equal, you can write an
extended proportion. Th e proportion ABGH 5
BC
HI 5
CD
IJ 5
AD
GJ is an extended proportion.
A scale factor is the ratio of corresponding linear measurements
of two similar fi gures. Th e ratio of the lengths of corresponding
sides BC and YZ , or more simply stated, the ratio of
corresponding sides, is BCYZ 5
20
8 5
5
2. So the scale factor
of nABC to nXYZ is 52 or 5 : 2.
Key Concept Similar Polygons
Defi ne
Two polygons are
similar polygons if
corresponding angles are
congruent and if the
lengths of corresponding
sides are proportional.
Diagram
ABCD , GHIJ
Symbols
/A > /G
/B > /H
/C > /I
/D > /J
ABGH 5
BC
HI 5
CD
IJ 5
AD
GJ
CB
A D
IH
G J
C X
Y
Z
B
A
ABC XYZ
15 20
25
6 8
10
Dynamic Activity
Similar Polygons
A
C T I V I T I
E S
D
S
AAAAAAAA
C
A
CC
I E
SSSSSSSS
DY
NAMIC
Lesson
Vocabulary
• similar fi gures
• similar polygons
• extended
proportion
• scale factor
• scale drawing
• scale
L
V
L
V
• s
LL
VVV
• s
a
W
r
c
t
You learned about
ratios in the last
lesson. Can you use
ratios to help you
solve the problem?
hsm11gmse_NA_0702.indd 440 4/15/09 1:49:41 PM
http://media.pearsoncmg.com/aw/aw_mml_shared_1/copyright.html
Problem 1
Got It?
Problem 2
Got It?
Lesson 7-2 Similar Polygons 441
Understanding Similarity
kMNP , kSRT
A What are the pairs of congruent angles?
/M > /S, /N > /R, and /P > /T
B What is the extended proportion for the ratios of
corresponding sides?
MNSR 5
NP
RT 5
MP
ST
1. DEFG , HJKL.
a. What are the pairs of congruent angles?
b. What is the extended proportion for the ratios of the lengths of
corresponding sides?
Determining Similarity
Are the polygons similar? If they are, write a similarity statement
and give the scale factor.
A JKLM and TUVW
Step 1 Identify pairs of congruent angles.
/J > /T, /K > /U, /L > /V, and /M > /W
Step 2 Compare the ratios of corresponding sides.
JK
TU 5
12
6 5
2
1
KL
UV 5
24
16 5
3
2
LMVW 5
24
14 5
12
7
JM
TW 5
6
6 5
1
1
Corresponding sides are not proportional, so the polygons are not similar.
B kABC and kEFD
Step 1 Identify pairs of congruent angles.
/A > /D, /B > /E , and /C > /F
Step 2 Compare t.

Similarities and congruences

This document discusses similarity and congruence of plane figures. It defines similar figures as those where corresponding angles are equal and corresponding side ratios are equal. Examples of similar figures include rectangles where the ratio of length to width is equal. The document provides examples of similar and congruent triangles and quadrilaterals. It also lists key terms and learning objectives related to identifying similar and congruent plane figures based on corresponding side lengths and angles.

7 4 Similar Triangles and t-5

This document discusses three rules for determining if triangles are similar: the AA Similarity Postulate, SAS Similarity Theorem, and SSS Similarity Theorem. It provides examples of applying each rule to determine if triangles are similar, and if so, writing the similarity statement and ratio.

Congruent and similar triangle by ritik

This document discusses congruent and similar triangles. It begins by introducing the concepts and explaining how recognizing similar shapes can simplify design work. It then defines congruent triangles as having equal sides and angles, while similar triangles have the same shape but not necessarily the same size. The document notes that two figures can be similar but not congruent, but not vice versa. It provides examples of similar and congruent figures. It further explains that similar triangles have corresponding sides and angles in the same locations that are in the same ratio. It demonstrates using ratios and proportions to determine unknown side lengths in similar figures. Finally, it discusses ways to prove triangles are similar, including having congruent corresponding angles (AA similarity) or proportional corresponding sides (SS

Polygons b.ing math. citra

This document discusses polygons and tessellations. It defines polygons, their properties including interior angles and the relationship between number of sides and total interior angle measures. Regular polygons are introduced as those with all congruent sides and interior angles. Methods for drawing regular polygons using angles and a circumscribed circle are provided. Tessellations are defined as arrangements that cover a region without gaps or overlaps. Regular hexagons, squares, and equilateral triangles can tessellate on their own. Problem solving involves calculating the measure of each interior angle of a regular hexagon.

Math chart model lesson

This powerpoint is a good tool to use to reintroduce students to the parts of the reference chart, so that they can effectively use it.

Project report on maths

This document defines and explains properties of various quadrilaterals and triangles. It defines parallelograms, rectangles, rhombi, and trapezoids, listing their key properties such as opposite sides being parallel and congruent, opposite angles being congruent, diagonals bisecting each other, etc. It also defines scalene, isosceles, equilateral, acute, obtuse, and congruent triangles. Area formulas are provided for various shapes using base and height.

Obj. 17 Congruent Triangles

Identify congruent parts based on a congruence relationship statement
Identify and prove congruent triangles given
Three pairs of congruent sides (Side-Side-Side)
Two pairs of congruent sides and a pair of congruent included angles (Side-Angle-Side)

Triangles

1) The document discusses properties and theorems related to triangles, including similarity, congruence, medians, altitudes, angle bisectors, and the Pythagorean theorem.
2) It provides criteria for establishing similarity between triangles, including having equal corresponding angles or proportional corresponding sides.
3) Theorems are presented on parallel lines cutting across two sides of a triangle in the same ratio, and on perpendiculars drawn from right triangle vertices cutting the hypotenuse.

02 geometry

This document provides definitions and formulas for calculating geometric properties of basic two-dimensional shapes such as triangles, rectangles, circles, trapezoids, and parallelograms. It also includes formulas for calculating volumes and surface areas of three-dimensional objects like cubes, spheres, cylinders, cones, and pyramids. Additionally, it discusses properties related to angles of intersection for lines and parallel lines, angle relationships in triangles, similarity of triangles, and the Pythagorean theorem.

Modern Geometry Topics

This powerpoint includes:
Triangles and Quadrangles
Definition, Types, Properties, Secondary part, Congruency and Area
Definitions of Triangles and Quadrangles
Desarguesian Plane
Mathematician Desargues and His Background
Harmonic Sequence of Points/Lines
Illustrations and Animated Lines.

Similar Triangles Notes

1) Congruent and similar triangles can be used to simplify design and calculations. Congruent triangles have equal sides and angles, while similar triangles have the same shape but not necessarily the same size.
2) Corresponding sides and angles of similar triangles have the same ratios. Ratios can be used to determine unknown side lengths.
3) Triangles are similar if two angles are congruent (AA similarity) or if all three sides are proportional (SSS similarity).

Geometry In The Real World

This document defines common geometric terms including point, line, plane, angle, perpendicular lines, parallel lines, triangles, right triangles, pentagons, hexagons, squares, rectangles, trapezoids, parallelograms, circles, cylinders, spheres, pyramids, cubes, and cones. It provides the basic definitions for these terms, stating that points have no size, lines have no thickness, planes extend forever, and polygons have a certain number of sides.

Triangles X CLASS CBSE NCERT

This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of similar triangles, including the AAA, SSS, SAS, and AA similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles discussed include scalene, isosceles, equilateral, acute, obtuse, and right triangles.

Triangle ppt

This document provides an overview of triangles, including definitions, types, properties, secondary parts, congruency, and area calculations. It defines a triangle as a 3-sided polygon with three angles and vertices. Triangles are classified by side lengths as equilateral, isosceles, or scalene, and by angle measures as acute, obtuse, or right. Key properties discussed include the angle sum theorem, exterior angle theorem, and Pythagorean theorem. Secondary parts like medians, altitudes, perpendicular bisectors, and angle bisectors are also defined. Tests for triangle congruency such as SSS, SAS, ASA, and RHS are outlined. Formulas are provided for calculating the areas of

Triangles introduction class 5

This document discusses triangles and their properties. It defines a triangle as a shape with three connected line segments and three vertices. The key properties discussed are:
1) The sum of the three interior angles of any triangle is always 180 degrees.
2) For a shape to be a triangle, the length of any one side must be less than the sum of the other two sides.
3) Triangles can be categorized based on the lengths of their sides (scalene, isosceles, equilateral) or degrees of their angles (acute, right, obtuse).

Geometry In The Real World Project

The document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, spheres, cylinders, cones, prisms and more. It provides the key properties of each shape such as the number of sides, angles, parallel or perpendicular lines, and other distinguishing characteristics.

Lecture 4.4

This document discusses two postulates for proving triangles congruent: the Side-Side-Side (SSS) postulate and the Side-Angle-Side (SAS) postulate. It provides examples of proofs using each postulate, demonstrating how to prove triangles congruent by showing that three sides or two sides and the included angle are congruent between the two triangles. The document includes practice problems applying these postulate proofs.

Surface area of prisms and cylinders

This amazing power point will show you everything that you need to know about finding the surface area of prisms and cylinders. 7TH GRADE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

CLASS X MATHS

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in the same ratio. Similar triangles have the same shape but not necessarily the same size. The document provides examples of determining if triangles are similar by checking if their corresponding angles are equal. It also shows using scale factors to calculate missing side lengths in similar triangles using the Basic Proportionality Theorem.

5.1 Congruent Polygons

Two polygons are congruent if they have the same shape and size, with corresponding angles and sides in the same position. Congruent polygons have corresponding angles that are equal and corresponding sides that are equal. The student learns to write and interpret congruence statements between triangles using equal corresponding angles and sides, and to prove polygons are congruent using the definition of congruence.

Similarities and congruences

Similarities and congruences

7 4 Similar Triangles and t-5

7 4 Similar Triangles and t-5

Congruent and similar triangle by ritik

Congruent and similar triangle by ritik

Polygons b.ing math. citra

Polygons b.ing math. citra

Math chart model lesson

Math chart model lesson

Project report on maths

Project report on maths

Obj. 17 Congruent Triangles

Obj. 17 Congruent Triangles

Triangles

Triangles

02 geometry

02 geometry

Modern Geometry Topics

Modern Geometry Topics

Similar Triangles Notes

Similar Triangles Notes

Geometry In The Real World

Geometry In The Real World

Triangles X CLASS CBSE NCERT

Triangles X CLASS CBSE NCERT

Triangle ppt

Triangle ppt

Triangles introduction class 5

Triangles introduction class 5

Geometry In The Real World Project

Geometry In The Real World Project

Lecture 4.4

Lecture 4.4

Surface area of prisms and cylinders

Surface area of prisms and cylinders

CLASS X MATHS

CLASS X MATHS

5.1 Congruent Polygons

5.1 Congruent Polygons

J9 b06dbd

This document provides information about similar and congruent figures in geometry. It defines similar figures as those that have the same shape but not necessarily the same size, while congruent figures have both the same shape and the same size. Corresponding parts of similar figures, such as corresponding angles and sides, are identified and their properties are described. Examples are provided to demonstrate how to determine if figures are similar based on ratios of corresponding side lengths. Congruent figures are also discussed, noting that corresponding angles and sides of congruent figures are congruent. The document concludes with practice problems applying the concepts of similar and congruent figures.

440 Chapter 7 SimilaritySimilar Polygons7-2Objective.docx

440 Chapter 7 Similarity
Similar Polygons7-2
Objective To identify and apply similar polygons
A movie theater screen is in the shape of
a rectangle 45 ft wide by 25 ft high.
Which of the TV screen formats at the
right do you think would show the most
complete scene from a movie shown on the
theater screen? Explain.
Similar fi gures have the same shape but not necessarily the same size. You can
abbreviate is similar to with the symbol ,.
Essential Understanding You can use ratios and proportions to decide whether
two polygons are similar and to fi nd unknown side lengths of similar fi gures.
You write a similarity statement with corresponding vertices in order, just as you write
a congruence statement. When three or more ratios are equal, you can write an
extended proportion. Th e proportion ABGH 5
BC
HI 5
CD
IJ 5
AD
GJ is an extended proportion.
A scale factor is the ratio of corresponding linear measurements
of two similar fi gures. Th e ratio of the lengths of corresponding
sides BC and YZ , or more simply stated, the ratio of
corresponding sides, is BCYZ 5
20
8 5
5
2. So the scale factor
of nABC to nXYZ is 52 or 5 : 2.
Key Concept Similar Polygons
Defi ne
Two polygons are
similar polygons if
corresponding angles are
congruent and if the
lengths of corresponding
sides are proportional.
Diagram
ABCD , GHIJ
Symbols
/A > /G
/B > /H
/C > /I
/D > /J
ABGH 5
BC
HI 5
CD
IJ 5
AD
GJ
CB
A D
IH
G J
C X
Y
Z
B
A
ABC XYZ
15 20
25
6 8
10
Dynamic Activity
Similar Polygons
A
C T I V I T I
E S
D
S
AAAAAAAA
C
A
CC
I E
SSSSSSSS
DY
NAMIC
Lesson
Vocabulary
• similar fi gures
• similar polygons
• extended
proportion
• scale factor
• scale drawing
• scale
L
V
L
V
• s
LL
VVV
• s
a
W
r
c
t
You learned about
ratios in the last
lesson. Can you use
ratios to help you
solve the problem?
hsm11gmse_NA_0702.indd 440 4/15/09 1:49:41 PM
http://media.pearsoncmg.com/aw/aw_mml_shared_1/copyright.html
Problem 1
Got It?
Problem 2
Got It?
Lesson 7-2 Similar Polygons 441
Understanding Similarity
kMNP , kSRT
A What are the pairs of congruent angles?
/M > /S, /N > /R, and /P > /T
B What is the extended proportion for the ratios of
corresponding sides?
MNSR 5
NP
RT 5
MP
ST
1. DEFG , HJKL.
a. What are the pairs of congruent angles?
b. What is the extended proportion for the ratios of the lengths of
corresponding sides?
Determining Similarity
Are the polygons similar? If they are, write a similarity statement
and give the scale factor.
A JKLM and TUVW
Step 1 Identify pairs of congruent angles.
/J > /T, /K > /U, /L > /V, and /M > /W
Step 2 Compare the ratios of corresponding sides.
JK
TU 5
12
6 5
2
1
KL
UV 5
24
16 5
3
2
LMVW 5
24
14 5
12
7
JM
TW 5
6
6 5
1
1
Corresponding sides are not proportional, so the polygons are not similar.
B kABC and kEFD
Step 1 Identify pairs of congruent angles.
/A > /D, /B > /E , and /C > /F
Step 2 Compare t.

Chapter 1.1

The document discusses properties of similar figures and how to determine if two figures are similar. It provides examples of similar figures and how to use scale factors and proportional sides to determine missing side lengths. Some key points made include:
- Two figures are similar if corresponding angles have the same measure and ratios of corresponding sides are equal.
- The scale factor is the ratio of corresponding sides and can be used to determine unknown side lengths of similar figures.
- Examples show determining if figures are similar and calculating missing side lengths using scale factors and proportional sides.

Text 10.5 similar congruent polygons

Two polygons are similar if they have the same shape but not necessarily the same size. Congruent polygons have the same shape and the same size. The document provides examples of finding corresponding sides and angles of similar and congruent polygons. It also gives examples of determining if two polygons are similar by checking if the ratios of corresponding sides are equal.

Geometry unit 7.2

This document is about similarity and similar polygons from a Holt Geometry textbook. It defines similar polygons as polygons with congruent angles and proportional side lengths. Examples are provided to identify similar polygons and write similarity statements. The similarity ratio of two similar polygons is defined as the ratio of corresponding side lengths. Applications include using proportions to find the length of a model based on its similarity to an actual object.

fjjh

The document defines similar polygons as polygons where corresponding angles are congruent and the ratios of corresponding sides are equal. It provides examples of similar triangles and scale factors. Similar shapes will have congruent corresponding angles and proportional corresponding sides, as demonstrated through examples finding missing side lengths and perimeter ratios of similar polygons.

Hoho

The document provides information on mathematical formulas for calculating the area of squares, rectangles, and triangles as well as the perimeter of polygons. It states that the area of a square can be calculated as s2, where s is the length of one side. The area of a rectangle can be found using the diagonals method, which is half the product of the two equal diagonal lengths. It also provides the formula for calculating the perimeter of a regular polygon as ns, where n is the number of sides and s is the length of one side. Finally, it shares the formula for calculating the area of a triangle using the x and y coordinates of its three vertices.

9 7 perimeters and similarity

This document discusses perimeters and similarity of triangles. It introduces scale factors and explains that if two triangles are similar, then the ratios of their corresponding sides are equal and the ratios of their corresponding perimeters are proportional to the ratios of their corresponding sides. It provides examples of calculating scale factors between similar triangles and using scale factors to determine missing side lengths or perimeters. The document establishes that the ratio found by comparing measures of corresponding sides of similar triangles is called the constant of proportionality or scale factor.

Chapter 6 Section 3 Similar Figures

The document discusses similar figures and scale drawings. It provides examples of using proportions to solve problems involving similar figures, scale drawings, and indirect measurements. Key concepts covered include: similar figures having the same shape but not necessarily the same size, with corresponding angles and sides in proportion; using proportions to solve problems involving similar figures and scale drawings; and using similar triangles to indirectly measure quantities like the height of a tree or flagpole using shadow lengths.

Congr similar

This document defines and provides examples of polygons, congruent polygons, and similar polygons. It begins by defining a polygon as a plane figure with three or more sides, and notes there are different types including convex, concave, and regular polygons. It then defines congruent polygons as having the same size and shape, and similar polygons as having the same shape but different sizes, with corresponding angles and sides that are proportional. Examples are provided to illustrate finding side lengths of similar polygons using size-change factors.

Geom jeopardy ch 8 review

The document discusses similar triangles and proportions. It includes questions about solving proportions, finding similarity ratios, determining if triangles are similar, finding corresponding sides of similar triangles given additional information like areas, and calculating values of variables in proportions involving similar figures.

Chapter 1.2

- Hales, a Greek mathematician, was the first to measure the height of a pyramid using similar triangles. He showed that the ratio of the height of the pyramid to the height of the worker was the same as the ratio of the heights of their respective shadows.
- The document discusses using similar triangles to solve problems involving finding unknown lengths, such as measuring the height of a pyramid based on the shadow lengths of the pyramid and a worker of known height.
- Examples are provided of determining if two triangles are similar based on proportional sides or equal corresponding angles, and using similarities between triangles to find unknown lengths.

Chapter 7

The document provides examples and step-by-step explanations for solving geometry problems involving similar and congruent shapes using transformations and properties of similarity and congruence. In one example, it is determined that two triangles are similar because corresponding angles are congruent. In another example, transformations of a rotation and translation are used to show that two figures are congruent.

Similar triangles

The document discusses similar triangles and how to use proportions to solve problems involving similar triangles. It provides examples of setting up proportions between corresponding sides of similar triangles to determine unknown side lengths. It also gives examples of applying similar triangle proportions to solve real-world problems involving shadows.

2.6.1 Congruent Triangles

Two triangles are congruent if their corresponding angles are equal and their corresponding sides are equal. The order of the vertices in a congruence statement indicates the matching parts between the triangles. If two triangles are congruent, then their corresponding parts will be equal.

Congruent and similar triangle by ritik

This document discusses congruent and similar triangles. It defines that congruent triangles have all sides and angles equal, while similar triangles have the same shape but not necessarily the same size. It explains that two figures can be similar but not congruent, but not the other way around. It then discusses how to determine if triangles are similar using corresponding sides, angles, ratios, and proportions. Specifically, it states that if two triangles have two congruent angles or all sides proportional, then the triangles are similar.

2.7.1 Congruent Triangles

* Write and interpret congruence statements
* Use properties of congruent triangles
* Prove triangles congruent using the definition of congruence

Ratios, proportions, similar figures

1) Ratios and proportions are used in many areas including map reading, scale drawings, and solving problems.
2) A ratio compares two quantities by division, and ratios that make the same comparison are equivalent ratios. Proportions are equations that state two ratios are equal.
3) Similar figures have the same shape but not necessarily the same size, with corresponding angles being congruent and corresponding sides forming equivalent ratios. Ratios and proportions can be used to solve for unknown sides or quantities in similar figures.

classification of quadrilaterals grade 9.pptx

This document defines and compares different types of quadrilaterals: parallelograms, rhombi, rectangles, squares, trapezoids, and kites. It provides properties and examples of each shape. Key points include: a parallelogram has two pairs of parallel opposite sides; a rhombus is a parallelogram with four congruent sides; a rectangle is a parallelogram with four right angles; a square has properties of both a rectangle and rhombus; a trapezoid has at least one pair of parallel sides; and a kite has two pairs of congruent consecutive sides. The document also covers angle sums, using properties to solve problems, and includes a logo

Ratios and Proportions.pptx

This document discusses ratios, proportions, and their uses. It provides examples of ratios comparing quantities like shaded area to unshaded area in rectangles. Proportions are defined as ratios that are equal, such as fractions that reduce to the same value. Examples are given for solving proportions to find unknown values. Similar figures are discussed as having the same shape but not necessarily the same size, with corresponding angles being congruent and sides proportional. Methods are presented for using proportions to solve for unknown sides or values in similar or scaled figures.

J9 b06dbd

J9 b06dbd

440 Chapter 7 SimilaritySimilar Polygons7-2Objective.docx

440 Chapter 7 SimilaritySimilar Polygons7-2Objective.docx

Chapter 1.1

Chapter 1.1

Text 10.5 similar congruent polygons

Text 10.5 similar congruent polygons

Geometry unit 7.2

Geometry unit 7.2

fjjh

fjjh

Hoho

Hoho

9 7 perimeters and similarity

9 7 perimeters and similarity

Chapter 6 Section 3 Similar Figures

Chapter 6 Section 3 Similar Figures

Congr similar

Congr similar

Geom jeopardy ch 8 review

Geom jeopardy ch 8 review

Chapter 1.2

Chapter 1.2

Chapter 7

Chapter 7

Similar triangles

Similar triangles

2.6.1 Congruent Triangles

2.6.1 Congruent Triangles

Congruent and similar triangle by ritik

Congruent and similar triangle by ritik

2.7.1 Congruent Triangles

2.7.1 Congruent Triangles

Ratios, proportions, similar figures

Ratios, proportions, similar figures

classification of quadrilaterals grade 9.pptx

classification of quadrilaterals grade 9.pptx

Ratios and Proportions.pptx

Ratios and Proportions.pptx

Geo 7-1 Ratios and Proportions

The document discusses ratios, proportions, and how to write and solve them. It provides examples of writing ratios for measurements like width to height. It also demonstrates how to set up and solve proportions using variables, cross products, and equations to find missing values like angle measures when given a ratio relationship. Examples include finding side lengths of triangles when the extended ratio and perimeter are given.

Geometry 1-7 Constructions

This document introduces geometric constructions using a straightedge and compass. It defines key terms like straightedge, compass, and construction. The objectives are for students to be able to make basic constructions to copy segments and angles, bisect segments and angles, and construct perpendicular lines. Links are provided for online instructions on various geometric constructions.

Angle Sum Theorem

This document discusses polygons and quadrilaterals. It introduces the Angle Sum Theorem, which states that the sum of the interior angles of an n-gon is (n-2)180. It also presents the Polygon Exterior Angle Theorem, which says that the sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. The document provides examples of applying these theorems and assigns homework problems related to polygons and quadrilaterals.

Bullying Prevention Certification

This certificate of completion recognizes that Jessica Tentinger from Urbandale attended a bullying prevention training on July 16, 2013. It provides her contact information, folder number, and notes that she does not have a nursing license. The certificate documents her participation in a bullying prevention activity.

Ethics

This certificate of completion recognizes that Jessica Tentinger from Urbandale attended an ethics training for Iowa educators on July 5th, 2013. It provides her folder number, notes that she does not have a nursing license, and specifies the training was on ethics for educators in Iowa.

Shipley - Algebra II Ch3 Proficiency Charts

This document contains test score data from multiple Algebra II classes on their chapter 3 exam and retake exam. It shows the distribution of scores on scatter plots for the original and retake exams for 2nd hour, 3rd hour, 5th hour, and 8th hour classes. The number of students who retook each exam is also provided.

Shipley - Algebra II Ch2 Proficiency Charts

The document contains test score data from multiple Algebra II classes on their chapter 2 exam and retake exam. Bar graphs show the distribution of scores on the initial test and retake for each class, along with the number of students who retook the test. This data allows comparison of student performance on the chapter 2 material across different class periods and on the retake exam.

Shipley - Semester 1 Summary Data

The document contains graphs showing the percentage of students achieving over 80% proficiency in various chapters, chapter reviews (Ch1R, Ch2R, etc.), and final exams for four different class periods (2nd hour, 3rd hour, 5th hour, 8th hour) during semester 1. For each chapter and assessment, the graphs indicate the percentage of students scoring over 80% proficiency. Performance varied across class periods and assessments, with proficiency generally higher on chapter reviews compared to initial chapter material and higher on semester 1 finals compared to individual chapter assessments.

Ch4 Matrices - How to use the Calculator

1) The document provides step-by-step instructions for entering matrices and performing matrix operations like determinant and inverse on a TI-84 graphing calculator.
2) It also shows how to set up and solve a system of equations using the calculator by writing the system as an augmented matrix, performing row reduced echelon form, and reading off the solutions.
3) Key steps include entering the matrix dimensions and elements, using menu options to calculate the determinant and inverse, and setting up and solving the system of equations as an augmented matrix.

Pre-observation Form Oct 2013

Jessica Tentinger will teach Algebra II to her 5th hour class at Urbandale High School. She will use direct instruction and small group work to teach students how to solve systems of equations in three variables by elimination and substitution. During the lesson, some students will receive direct instruction while others work independently or in small groups. The teacher will check for understanding informally by asking questions and reviewing homework, and formally through an upcoming test. The administrator is asked to observe student engagement during both whole-class instruction and independent work time.

Algebra II Classroom and Homework Expectations

The Algebra II class uses a student-centered, self-paced model where students work at their own pace to learn material. Lessons are short but provide necessary content, then students work independently or in small groups on practice problems while receiving one-on-one help from the teacher. Homework consists of worksheets for students to complete problems until they understand concepts. Assignments are graded for completion, and students are responsible for their own learning by asking questions when stuck.

Sina workshop, day 1, january 25, 2013

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Iowa Assessment Math Growth Rates Grades 7-11th

- 42 students in Geometry were tested and enrolled for the full 2011-2012 academic year. 60% of students met or exceeded expected growth targets, while 19% made growth but did not meet expected targets and 21% showed negative growth.
- 1 student was tested in Algebra 2 and enrolled for the full year. This student made growth but did not meet the expected growth target.
- Data provided achievement results for students in Geometry and Algebra 2 classes from the 2011-2012 school year. The majority of Geometry students met growth targets, while the single Algebra 2 student grew but did not reach the expected level.

Geometry Chapter 3 Test Scores and Retake Test

This blank score sheet is for a geometry class taught by Ms. J. Tentingger during the first quarter. It lists the date and leaves spaces for a student's name and scores on various assignments and tests. No other information is provided on the document.

Alg II 3-6 Solving Systems - Matrices

This document discusses representing and solving systems of linear equations using matrices. It defines what a matrix is and how to identify matrix elements. A system of equations can be represented by a matrix with each row representing an equation and each column representing a variable, except the last column which holds the constants. To solve the system, the matrix is row reduced into reduced row echelon form through operations like row switching, scalar multiplication, and row addition. The solutions can then be read from the reduced matrix. Graphing calculators can also use the rref function to row reduce a matrix representing a system of equations and directly give the solutions.

Alg II 3-5 Sytems Three Variables

Three variable systems of equations can be solved using elimination or substitution similarly to two variable systems. For elimination, equations are paired to eliminate one variable, resulting in two equations with two unknowns that can then be solved. For substitution, one equation is solved for one variable in terms of others and substituted into the remaining equations to yield a system that can be solved. An example application involving budgets shirts is worked through to demonstrate solving a three variable system.

Alg II 3-4 Linear Programming

The document discusses the process of linear programming which involves defining variables, writing constraints as inequalities, graphing the feasible region, finding the vertices, writing an objective function, substituting the vertices into the function, and determining the maximum or minimum value. It provides two examples of using linear programming to maximize profits by determining the optimal number of acres to plant different crops or units of steel to produce.

Alg II 3-3 Systems of Inequalities

This document provides an overview of solving systems of linear inequalities through graphing and tables. It defines a system of inequalities as a set of inequalities where the solution satisfies all inequalities. Two main methods are discussed: using a table to systematically substitute values to find solutions, and graphing the inequalities as half-planes to find the overlap region as the solution. Several examples are provided and solved to illustrate these concepts. Key objectives are to be able to solve systems of linear inequalities and represent the solutions graphically.

Alg II 3-2 Solving Systems Algebraically

This document provides an overview of solving systems of linear equations algebraically. There are two main methods: substitution and elimination. Substitution involves isolating one variable and substituting it into the other equation. Elimination involves adding or subtracting equations to eliminate one variable. Examples are provided to demonstrate both methods. The objectives are for students to be able to solve linear systems algebraically and relate it to representing relationships between quantities with graphs and equations.

Geo 7-1 Ratios and Proportions

Geo 7-1 Ratios and Proportions

Geometry 1-7 Constructions

Geometry 1-7 Constructions

Angle Sum Theorem

Angle Sum Theorem

Bullying Prevention Certification

Bullying Prevention Certification

Ethics

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Shipley - Algebra II Ch3 Proficiency Charts

Shipley - Algebra II Ch3 Proficiency Charts

Shipley - Algebra II Ch2 Proficiency Charts

Shipley - Algebra II Ch2 Proficiency Charts

Shipley - Semester 1 Summary Data

Shipley - Semester 1 Summary Data

Ch4 Matrices - How to use the Calculator

Ch4 Matrices - How to use the Calculator

Pre-observation Form Oct 2013

Pre-observation Form Oct 2013

Formal Observation/Notes October 2013

Formal Observation/Notes October 2013

Algebra II Classroom and Homework Expectations

Algebra II Classroom and Homework Expectations

Sina workshop, day 1, january 25, 2013

Sina workshop, day 1, january 25, 2013

Iowa Assessment Math Growth Rates Grades 7-11th

Iowa Assessment Math Growth Rates Grades 7-11th

Geometry Chapter 3 Test Scores and Retake Test

Geometry Chapter 3 Test Scores and Retake Test

Alg II 3-6 Solving Systems - Matrices

Alg II 3-6 Solving Systems - Matrices

Alg II 3-5 Sytems Three Variables

Alg II 3-5 Sytems Three Variables

Alg II 3-4 Linear Programming

Alg II 3-4 Linear Programming

Alg II 3-3 Systems of Inequalities

Alg II 3-3 Systems of Inequalities

Alg II 3-2 Solving Systems Algebraically

Alg II 3-2 Solving Systems Algebraically

HYPERTENSION - SLIDE SHARE PRESENTATION.

IT WILL BE HELPFULL FOR THE NUSING STUDENTS
IT FOCUSED ON MEDICAL MANAGEMENT AND NURSING MANAGEMENT.
HIGHLIGHTS ON HEALTH EDUCATION.

A Visual Guide to 1 Samuel | A Tale of Two Hearts

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Chapter wise All Notes of First year Basic Civil Engineering.pptx

Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1

A Independência da América Espanhola LAPBOOK.pdf

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(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.

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- 2. Students will be able to identify and apply similar polygons
- 3. You can use ratios and proportions to decide whether two polygons are similar and to find unknown side lengths of similar figures.
- 4. Have the same shape but not necessarily the same size Is similar to is abbreviated by ~ symbol Two Polygons are similar if corresponding angles are congruent and the corresponding sides are proportional
- 5. Like congruence statements, the order matters so if two figures are similar, their corresponding parts should be in the same order If ΔABC ~ ΔDEG then <A ≅ <D and AB ~ DE
- 6. Use when three or more ratios are equal AB = BC = CD = AD GH HI IJ GJ Scale Factor: ratio of corresponding linear measurements to two similar figures (ratio of corresponding sides in simplest form)
- 7. What are the pairs of congruent angles if ΔABC ~ ΔRST? What is the extended proportion for the ratios of corresponding sides for ΔABC ~ ΔRST?
- 11. ABCD ~ EFGD What is the value of x? What is the value of y?
- 13. Your class is making a poster for a rally. The poster’s design is 6in. high by 10 in. wide. The space allowed for the poster is 4 ft high by 8ft wide. What are the dimensions for the largest poster that will fit in the space? What if the dimensions of the largest space was 3 ft high by 4 ft wide?
- 15. All lengths are proportional to their corresponding actual lengths Scale: ratio that compares each length in the scale drawing to the actual length Where have you seen a scale?
- 16. The diagram shows a scale drawing of the Golden Gate Bridge. The distance between the two towers is the main span. What is the actual length of the main span of the bridge if it is 6.4 cm in the drawing?
- 17. Pg. 375 # 1 – 18, 21 – 28, 32 27 Problems